Apparatus for detecting failure of exhaust gas sensor utilizing element temperature

ABSTRACT

An apparatus for detecting a failure of an exhaust gas sensor disposed in an exhaust manifold is provided. The apparatus comprises a control unit. The control unit compares detection values of the exhaust gas sensor detected under different element temperatures of the exhaust gas sensor. The control unit detects a failure of the exhaust gas sensor based on the comparison result. In one embodiment, the different states include a state in which the element temperature is maintained at higher level and a state in which the element temperature is maintained at lower level. The element temperature can be controlled by a response assignment control scheme. In one embodiment, the detection values are subjected to a filtering process and/or a statistical process using a successive least squares method. The control unit compares the statistically processed detection values to detect a failure of the exhaust gas sensor.

BACKGROUND OF THE INVENTION

[0001] 1. Technical Field

[0002] The present invention relates to an apparatus and a method for controlling an element temperature of an exhaust gas sensor disposed in an exhaust system of an internal combustion engine to detect a failure of the exhaust gas sensor.

[0003] 2. Description of the Related Art

[0004] A catalyst converter is provided in an exhaust system of an internal combustion engine of a vehicle. When the air-fuel ratio of air-fuel mixture introduced into the engine is lean, the catalyst converter oxidizes HC and CO with excessive oxygen included in the exhaust gas. When the air-fuel ratio is rich, the catalyst converter reduces Nox with HC and CO. When the air-fuel ratio is in the stoichiometric air-fuel ratio region, HC, CO and Nox are simultaneously and effectively purified.

[0005] An exhaust gas sensor is provided downstream of the catalyst converter. The exhaust gas sensor detects the concentration of oxygen included in the gas that is discharged into the exhaust system. The detection value of the exhaust gas sensor is used for various control of the internal combustion engine. If response of the exhaust gas sensor deteriorates, the internal combustion engine may not be appropriately controlled, which may cause deterioration in the operating state of the engine.

[0006] Japanese Patent No. 2812252 discloses a method for detecting an abnormal state of an exhaust gas sensor based on the differential of the output of the exhaust gas sensor. When the number of times that the differential of an output of the exhaust gas sensor is great is less than a predetermined value, it is determined that the exhaust gas sensor is in an abnormal state. The method is based on the knowledge that the time-differential of the sensor output is often far from zero when the exhaust gas sensor is normal while the time-differential of the sensor output is always close to zero when the exhaust gas sensor is faulty.

[0007] Since the catalyst converter and the exhaust gas sensor are disposed in series, the output of the exhaust gas sensor is influenced by delay characteristics (low pass characteristics) of the catalyst. That is, the output of the exhaust gas sensor varies according to the degree of deterioration of the catalyst. In the above conventional scheme of analyzing variations in the time-differential of the output of the exhaust gas sensor, it is difficult to determine whether such variations are caused by changes in response characteristics of the catalyst or by changes in response characteristics of the exhaust gas sensor.

[0008] Therefore, there is a need for an apparatus and a method capable of detecting a failure of an exhaust gas sensor as distinguished from deterioration of catalyst. There is also a need for an apparatus and a method for detecting a failure of the exhaust gas sensor without discharging deleterious substances.

SUMMARY OF THE INVENTION

[0009] According to one aspect of the present invention, an apparatus for detecting a failure of an exhaust gas sensor provided in an exhaust manifold of an engine is provided. The apparatus comprises a control unit configured to compare detection values of the exhaust gas sensor under different temperatures of an element provided in the exhaust gas sensor.

[0010] The exhaust gas sensor comprises the element, which is typically zirconium (ZrO2) or titania (TiO2). The invention utilizes a characteristic that the output of the exhaust gas sensor varies according to the temperature of the element. When the element temperature is changed, the amount of change in the output of the exhaust gas sensor that is normal is different from the amount of change in the output of the exhaust gas sensor that is faulty. A failure of the exhaust gas sensor can be detected by watching the output of the exhaust gas sensor when the element temperature is changed. Such failure detection is not influenced by deterioration of the catalyst.

[0011] The air-fuel ratio does not need to be manipulated for the purpose of detecting a failure of the exhaust gas sensor. The failure detection can be done without increasing the amount of deleterious substances in the exhaust gas, which would otherwise be produced from manipulation of the air-fuel ratio for the purpose of the failure detection.

[0012] According to another aspect of the present invention, the control unit controls the element temperature of the exhaust gas sensor to generate the states of the different element temperatures. In one embodiment of the present invention, a state in which the element temperature is controlled to a first temperature for a normal operating state of the engine, and a state in which the element temperature is controlled to a second temperature lower than the first temperature are generated. When the element temperature for the normal operating state of the engine is sufficiently low, the element temperature may be increased so as to carry out the failure detection. Thus, when a failure of the exhaust gas sensor is detected, the element temperature can be controlled to a temperature that is different from the temperature used for the normal operating state of the engine.

[0013] According to another aspect of the present invention, the failure detection apparatus further comprises a filter for filtering the detection values of the exhaust gas sensor. The failure of the exhaust gas sensor is detected by comparing the filtered detection values of the exhaust gas sensor under different element temperatures. In one embodiment of the present invention, the filter includes a band-pass filter.

[0014] The filtering process can remove variations in the detection value of the exhaust gas sensor that are caused by changes in the air-fuel ratio. Furthermore, a portion of the power spectrum of the sensor output that has greater power is extracted. Thus, the influence of the air-fuel ratio control and the influence of noise are reduced to improve the accuracy of the failure detection.

[0015] According to another aspect of the present invention, a statistical process using a successive least squares method is applied to the detection values of the exhaust gas sensor. A failure of the exhaust gas sensor is detected by comparing the statistically processed detection values of the exhaust gas sensor under different element temperatures. In one embodiment, the statistical process using the successive least squares method is applied to the filtered detection values of the exhaust gas sensor.

[0016] The detection value of the exhaust gas sensor is influenced by noise and the operating state of the engine. The statistical process using the successive least squares method reduces such influence on the failure detection.

[0017] According to another aspect of the present invention, the detection values of the exhaust gas sensor are obtained when a vehicle on which the engine is mounted is at cruise. Since the detection values of the exhaust gas sensor are obtained in a state in which the element temperature is stable and the air-fuel ratio control is stable, the accuracy of detecting a failure of the exhaust gas sensor is improved.

[0018] According to another aspect of the present invention, the detection values of the exhaust gas sensor are obtained when the engine is in a predetermined operating state. The detection values of the exhaust gas sensor vary according to the operating state of the engine. By establishing a condition that the failure detection is performed under a predetermined operating state, such variations are suppressed, thereby improving the accuracy of the failure detection.

[0019] According to another aspect of the present invention, the control unit estimates the element temperature of the exhaust gas sensor. The control unit determines a duty ratio of energization of a heater disposed in the exhaust gas sensor based on the estimated element temperature. The element is heated by the heater. In the invention, the cost of providing an additional means for directly measuring the element temperature of the exhaust gas sensor is avoided. The estimation of the element temperature enables the element temperature to be controlled with better accuracy.

[0020] According to another aspect of the present invention, the control unit uses response assignment control to control the element temperature. The response assignment control prevents the element temperature from overshooting or undershooting. Thus, it is avoided that the element is damaged due to excessively high temperature. It is further avoided that the element is inactivated due to excessively low temperature. By performing the response assignment control, the accuracy of controlling the element temperature is maintained at high level, thereby improving the durability of the heater.

BRIEF DESCRIPTION OF THE DRAWINGS

[0021]FIG. 1 is a schematic view of an internal combustion engine and its controller according to one embodiment of the present invention.

[0022]FIG. 2 is a view of layout of a catalyst apparatus and an exhaust gas sensor according to one embodiment of the present invention.

[0023]FIG. 3 shows one example of a frequency response of an output of the exhaust gas sensor.

[0024]FIG. 4 shows that a frequency response of an output of an exhaust gas sensor varies according to the degree of deterioration of catalyst.

[0025]FIG. 5 shows that a frequency response of a filtered output of an exhaust gas sensor according to the degree of deterioration of catalyst.

[0026]FIG. 6 shows one example of output characteristics of an exhaust gas sensor that vary according to an element temperature.

[0027]FIG. 7 shows behavior of an output of an exhaust gas sensor that varies according to an element temperature.

[0028]FIG. 8 shows a frequency response of an output of an exhaust gas sensor that varies according to an element temperature.

[0029]FIG. 9 shows an output of an exhaust gas sensor that varies according to both an element temperature and a fail/normal state of the exhaust gas sensor.

[0030]FIG. 10 shows filter characteristics of a band-pass filter according to one embodiment of the present invention.

[0031]FIG. 11 shows an output of an exhaust gas sensor and a frequency response under different element temperatures.

[0032]FIG. 12 is a functional block diagram of a failure detection apparatus in accordance with one embodiment of the present invention.

[0033]FIG. 13 is a control block diagram of an element temperature controller in accordance with one embodiment of the present invention.

[0034]FIG. 14 schematically shows a switching line for response assignment control in accordance with one embodiment of the present invention.

[0035]FIG. 15 shows response characteristics of a controlled quantity that depend on a setting parameter of a switching function in response assignment control in accordance with one embodiment of the present invention.

[0036]FIG. 16 shows one example of a steady exhaust gas temperature map used for estimating an element temperature in accordance with one embodiment of the present invention.

[0037]FIG. 17 schematically shows a flow for a failure detection process in accordance with one embodiment of the present invention.

[0038]FIG. 18 is a flowchart showing a main routine for a failure detection process in accordance with one embodiment of the present invention.

[0039]FIG. 19 is a flowchart showing a routine for a successive least squares method in accordance with one embodiment of the present invention.

[0040]FIG. 20 is a flowchart showing a failure detection routine in accordance with one embodiment of the present invention.

[0041]FIG. 21 is a flowchart showing an element temperature control routine in accordance with one embodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0042] Structure of Internal Combustion Engine and Controller

[0043] Preferred embodiments of the present invention will be described referring to the attached drawings. FIG. 1 is a block diagram showing a controller of an internal-combustion engine (hereinafter referred to as an engine) in accordance with one embodiment of the invention.

[0044] An electronic control unit (hereinafter referred to as an ECU) 5 comprises an input interface 5 a for receiving data sent from each part of the engine 1, a CPU 5 b for carrying out operations for controlling each part of the engine 1, a storage device 5 c including a read only memory (ROM) and a random access memory (RAM), and an output interface 5 d for sending control signals to each part of the engine 1. Programs and various data for controlling each part of the vehicle are stored in the ROM. A program for performing a failure detection process according to the invention, data and tables used for operations of the program are stored in the ROM. The ROM may be a rewritable ROM such as an EEPROM. The RAM provides work areas for operations by the CPU 5 a, in which data sent from each part of the engine 1 as well as control signals to be sent out to each part of the engine 1 are temporarily stored.

[0045] The engine is, for example, an engine equipped with four cylinders. An intake manifold 2 is connected to the engine 1. A throttle valve 3 is disposed upstream of the intake manifold 2. A throttle valve opening (θ TH) sensor 4, which is connected to the throttle valve 3, outputs an electric signal corresponding to an opening angle of the throttle valve 3 and sends it to the ECU 5.

[0046] A bypass passage 21 for bypassing the throttle valve 3 is provided in the intake manifold 2. A bypass valve 22 for controlling the amount of air to be supplied into the engine 1 is provided in the bypass passage 21. The bypass valve 22 is driven in accordance with a control signal from the ECU 5.

[0047] A fuel injection valve 6 is provided for each cylinder at an intermediate point in the intake manifold 2 between the engine 1 and the throttle valve 3. The fuel injection valve 6 is connected to a fuel pump (not shown) to receive fuel supplied from a fuel tank (not shown). The fuel injection valve 6 is driven in accordance with a control signal from the ECU 5.

[0048] An intake manifold pressure (Pb) sensor 8 and an outside air temperature (Ta) sensor 9 are mounted in the intake manifold 2 downstream of the throttle valve 3. The detected intake manifold pressure Pb and outside air temperature Ta are sent to the ECU 5.

[0049] An engine water temperature (TW) sensor 10 is attached to the cylinder peripheral wall, which is filled with cooling water, of the cylinder block of the engine 1. The temperature of the engine cooling water detected by the TW sensor is sent to the ECU 5.

[0050] A rotational speed (Ne) sensor 13 is attached to the periphery of the camshaft or the periphery of the crankshaft (not shown) of the engine 1, and outputs a CRK signal pulse at a predetermined crank angle cycle (for example, a cycle of 30 degrees) that is shorter than a TDC signal pulse cycle issued at a crank angle cycle associated with a TDC position of the piston. The CRK pulses are counted by the ECU 5 to determine the rotational speed Ne of the engine 1.

[0051] An exhaust manifold 14 is connected to the engine 1. The engine 1 discharges exhaust gas through the exhaust manifold 14. A catalyst converter 15 removes deleterious substances such as HC, CO, and Nox included in exhaust gas flowing through the exhaust manifold 14. The catalyst converter 15 comprises two catalysts, an upstream catalyst and a downstream catalyst.

[0052] A full range air-fuel ratio (LAF) sensor 16 is provided upstream of the catalyst converter 15. The LAF sensor 16 linearly detects the concentration of oxygen included in exhaust gas over a wide air-fuel ratio zone, from the rich zone where the air/fuel ratio is richer than the stoichiometric air/fuel ratio to an extremely lean zone. The detected oxygen concentration is sent to the ECU 5.

[0053] An O2 (exhaust gas) sensor 17 is provided between the upstream catalyst and the downstream catalyst. The O2 sensor 17 is a binary-type of exhaust gas concentration sensor. The O2 sensor outputs a high level signal when the air-fuel ratio is richer than the stoichiometric air-fuel ratio, and outputs a low level signal when the air-fuel ratio is leaner than the stoichiometric air-fuel ratio. The electric signal is sent to the ECU 5.

[0054] The O2 sensor comprises an element and a heater for heating the element. The element is implemented with, for example, zirconium (ZrO2) or titania (TiO2). The heater is connected to an electric circuit. The element temperature can be controlled by energization energy supplied to the heater.

[0055] A vehicle speed (VP) sensor 23 for detecting vehicle speed is connected to the ECU 5. The detected vehicle speed signal is sent to the ECU 5.

[0056] Signals sent to the ECU 5 are passed to the input circuit 5 a. The input interface 5 a converts analog signal values into digital signal values. The CPU 5 b processes the resulting digital signals, performs operations in accordance with the programs stored in the ROM, and creates control signals. The output interface 5 d sends these control signals to actuators for a bypass valve 22, fuel injection valve 6 and other mechanical components.

[0057]FIG. 2(a) shows a structure of the catalyst converter 15. Exhaust gas introduced into the exhaust manifold 14 passes through the upstream catalyst 25 and then through the downstream catalyst 26. It is known that it is easier to maintain the purification rate of Nox at an optimal level by air-fuel ratio control based on the output of an O2 sensor provided between the upstream and downstream catalysts, compared with air-fuel ratio control based on the output of an O2 sensor provided downstream of the downstream catalyst. Therefore, in the embodiment of the invention, the O2 sensor 17 is provided between the upstream and downstream catalysts. The O2 sensor 17 detects the concentration of oxygen included in exhaust gas after the passage through the upstream catalyst 25.

[0058]FIG. 2(b) is a block diagram showing a system from a LAF sensor 16 to the O2 sensor 17 shown in FIG. 2(a). The LAF sensor 16 detects an air-fuel ratio Kact of the exhaust gas supplied to the upstream catalyst 25. The O2 sensor 17 outputs a voltage Vout representing the oxygen concentration of the exhaust gas after the purification by the upstream catalyst 25.

[0059] The upstream catalyst 25 and the O2 sensor 17 are disposed in series. There exist delay and dead time of the upstream catalyst 25 and the O2 sensor 17 between an input of the system or the air-fuel ratio Kact and an output of the system or the output Vout of the O2 sensor 17.

[0060]FIG. 3 shows a result of Fourier transformation of the O2 sensor output Vout. If deterioration of the catalyst proceeds, the power spectrum of the sensor output Vout increases in the direction shown by an arrow 41. On the other hand, if the catalyst is a newer one, the power spectrum of the sensor output Vout decreases in the direction shown by an arrow 42. Based on this characteristic, deterioration of the catalyst can be determined.

[0061] If the O2 sensor deteriorates, a response delay of the O2 sensor increases. When the response delay increases, the power spectrum of the sensor output Vout decreases in the direction shown by the arrow 42.

[0062] Thus, when the O2 sensor deteriorates or is faulty, deterioration of the catalyst cannot be precisely detected since the power spectrum of the sensor output Vout decreases. In other words, a state in which the catalyst is new and a state in which the O2 sensor deteriorates cannot be distinguished by the power spectrum of the sensor output Vout.

[0063] Distinguishment of Deterioration of Catalyst from Failure of O2 Sensor

[0064] For the sake of easier understanding of the present invention, the scheme of distinguishing deterioration of the catalyst from a failure of the O2 sensor will be described. First, referring to FIGS. 4 and 5, the scheme of detecting deterioration of the catalyst will be described.

[0065]FIG. 4 shows a power spectrum of the O2 sensor output Vout (a) when the catalyst is new, (b) when the purification rate of the catalyst is sufficient, and (c) when the purification rate of the catalyst is insufficient. In FIGS. 4(a) to 4(c), the level of the power spectrum of the sensor output Vout in the frequency region of 3 through 7 Hz varies, which is indicated by the reference number 45.

[0066] FIGS. 5(a) to 5(c) show a result of filtering the sensor output Vout shown in FIGS. 4(a) to 4(c) with a band-pass filter, respectively. The power spectrum of the sensor output Vout in the frequency region of 3 through 7 Hz is emphasized by the filter. As shown by the reference number 46, as the catalyst deteriorates, the power spectrum of the sensor output Vout in the frequency regions 3 to 7 Hz increases. Thus, by evaluating the sensor output Vout in the frequency region of 3 to 7 Hz, it can be determined whether the catalyst is in a deteriorated state.

[0067] The concept of determining a failure of the O2 sensor will be described. FIG. 6 shows output characteristics (referred to as Z curve) of the O2 sensor. A curve 51 shows a case in which the element temperature is 600°. A curve 52 shows a case in which the element temperature is 700°. A curve 53 shows a case in which the element temperature is 800°. It is seen that the amount of change in the output Vout of the O2 sensor is greater as the element temperature is lower.

[0068]FIG. 7(a) shows behavior of the sensor output Vout when the element temperature is 600°. FIG. 7(b) shows behavior of the sensor output Vout when the element temperature is 800°. A graph 55 shows vehicle speed. Each of graphs 56 and 57 shows an output of the exhaust gas sensor. As seen from comparison between FIGS. 7(a) and 7(b), the amount of variation in the sensor output Vout when the element temperature is low is greater than the amount of variation in the sensor output Vout when the element temperature is high.

[0069]FIG. 8(a) shows a result of Fourier transformation of the sensor output Vout shown in FIG. 7(a). FIG. 8(b) shows a result of Fourier transformation of the sensor output Vout shown in FIG. 7(b). Because the amount of variation in the sensor output Vout is greater as the element temperature is lower, power of the sensor output Vout in each frequency also increases when the element temperature gets low.

[0070] In FIG. 9, a curve 62 shows a power spectrum of the sensor output Vout when the element temperature is 600° and the O2 sensor is faulty (e.g., delay characteristics of the O2 sensor are great). A curve 61 shows a power spectrum of the sensor output Vout when the element temperature is 600° and the O2 sensor is normal. A curve 63 shows a power spectrum of the sensor output Vout when the element temperature is 800° and the O2 sensor is normal.

[0071] It is seen that the power spectrum of the sensor output Vout increases when the element temperature decreases. The increase in the power spectrum when the O2 sensor is faulty is smaller than the increase when the O2 sensor is normal. Therefore, by comparing the sensor output Vout when the element temperature is low (in this example, 600°) with the sensor output Vout when the element temperature is high (in this example, 800°), it can be determined whether the O2 sensor is faulty. If a ratio between the sensor output Vout when the element temperature is low and the sensor output Vout when the element temperature is high is less than a predetermined value, it indicates that the O2 sensor is faulty.

[0072] According to the scheme, a failure of the O2 sensor can be detected without changing the air-fuel ratio for the purpose of failure detection, which would otherwise reduce the purification rate of the catalyst. The amount of deleterious substances in exhaust gas does not increase because the air-fuel ratio is intentionally changed for the failure detection.

[0073] In order to emphatically extract changes in the sensor output Vout when the element temperature is changed, a filtering process is applied to the sensor output Vout. FIG. 10 shows one example of filter characteristics of a band-pass filter used for the filtering process.

[0074] As shown in FIGS. 8 and 9, when the element temperature decreases, the power spectrum of the sensor output Vout increases in each frequency. However, as the frequency increases, the magnitude of the power spectrum in each frequency decreases due to low-pass characteristics of the catalyst and the O2 sensor. Since fluctuating components of the sensor output Vout at the time when the element temperature is changed need to be evaluated, it is preferable that steady components are removed. Therefore, a band-pass filter having characteristics as shown in FIG. 10 is used. In the example, the band-pass filter is designed to extract the power spectrum of the sensor output Vout in the frequency region of 0.1 to 1.0 Hz.

[0075]FIG. 11(a) shows behavior of the filtered sensor output Vout_f when the element temperature is 600°. FIG. 11(b) shows behavior of the filtered sensor output Vout_f when the element temperature is 800°. FIG. 11(c) shows a result of Fourier transformation of the filtered sensor outputs Vout shown in FIGS. 11(a) and 11(b). A graph 65 shows a power spectrum of the sensor output Vout_f when the element temperature is 600°. A graph 66 shows a power spectrum of the sensor output Vout_f when the element temperature is 800°. By carrying out the filtering process, changes in the sensor output Vout that are caused by changes in the element temperature can be extracted as an amplitude difference 67.

[0076] Thus, deterioration of the catalyst affects the power spectrum of the O2 sensor output in the frequency region of 3 to 7 Hz. The deterioration of the catalyst can be determined by comparing detection values of the O2 sensor in the frequency region. On the other hand, a failure of the O2 sensor is detected by comparing detection values of the O2 sensor under different element temperatures. Therefore, it is possible to clearly distinguish deterioration of the catalyst from a failure of the O2 sensor.

[0077] Structure of Failure Detection Apparatus

[0078]FIG. 12 is a functional block diagram showing an apparatus for detecting a failure of the O2 sensor according to one embodiment of the present invention. In a first pass, a state in which the element temperature is high is generated. A band-pass filter 72 is applied to the O2 sensor output. The band-pass filter 72 has characteristics as shown in FIG. 10. The band-pass filter 72 filters the sensor output Vout in accordance with equation (1) to generate Vout_f. Here, av1, av2, . . . , avn, bv0, bv1, . . . , bvm are filter coefficients predetermined by simulation or the like.

Vout_(—) f(k)=av1·Vout_(—) f(k−1)+av2·Vout_(—) f(k−2)+, . . . , +avn·Vout_(—) f(k−n)+bv0·Vout(k)+bv1·Vout(k−1)+, . . . , +bvm·Vout(k−m)   (1)

[0079] The filtered sensor output Vout_f(k) is squared by a multiplier 73 to generate Vout_fsq(k) as shown in equation (2).

Vout_(—) fsq(k)=Vout_(—) f(k)×Vout_(—) f(k)   (2)

[0080] Alternatively, a low pass filter may be used instead of the band-pass filter. Since a band-pass filter capable of passing low frequency components tends to be unstable, a high pass filter and a low pass filter may be applied sequentially.

[0081] A statistical processing section 74 applies a successive least squares method to the squared sensor output Vout_fsq in accordance with equations (3) through (6) to determine a statistically processed sensor output Vout_fsq_(—)1s.

Vout_(—) fsq _(—)1s(k)=Vout_(—) fsq _(—)1s(k−1)+KP(k)·Eo2(k)   (3)

[0082] An error Eo2(k) shown in the equation (3) is expressed by equation (4). A gain coefficient KP(k) is calculated in accordance with equation (5).

Eo2(k)=Vout_(—) fsq _(—)1s(k−1)−Vout_(—) fsq(k)   (4)

[0083] $\begin{matrix} {{{KP}(k)} = \frac{P(k)}{1 + {P(k)}}} & (5) \end{matrix}$

[0084] Here, “P” in the equation (5) is determined by equation (6). $\begin{matrix} {{P\left( {k + 1} \right)} = {\frac{1}{\lambda_{i}}{\left( {1 - \frac{\lambda_{2} \cdot {P(k)}}{\lambda_{i} + {\lambda_{2} \cdot {P(k)}}}} \right) \cdot {P(k)}}}} & (6) \end{matrix}$

[0085] Variations may occur in the O2 sensor output due to noise conditions. The sensor output may also vary according to the operating state of the vehicle/engine. The application of the successive least squares method can minimize the influence caused by such variations on the failure detection. Furthermore, by carrying out the successive least squares method, it is unnecessary to hold the filtered sensor output Vout_f after the statistical process in each cycle, thereby economizing on memory usage.

[0086] Alternatively, a non-successive least squares method may be used. The type of least squares method is determined by the values of λ₁ and λ₂ in the equation (6). For example, in a fixed gain method, λ₁=1 and λ₂=0. In a least-squares method, λ₁=1 and λ₂=1. In a decreasing gain method, λ₁=1 and λ₂=λ. In a weighted least squares method, λ₁=λ and λ₂=1.

[0087] Vout_fsq_(—)1s determined based on the sensor output Vout in a state in which the element temperature is high is held in a first memory 75 as Vout_fsq_(—)1s_H. Thus, the first pass is completed.

[0088] In a second pass, a state in which the element temperature is low is generated. In a similar way to the first pass with the state in which the element temperature is high, the O2 sensor output Vout is subjected to the band-pass filter 72, the multiplier 73 and the statistical processing section 74. The statistically processed sensor output Vout_fsq_(—)1s that is determined based on the sensor output Vout in the state in which the element temperature is low is held in a second memory 76 as Vout_fsq_(—)1s_L.

[0089] A failure determination section 77 reads out Vout_fsq_(—)1s_H and Vout_fsq_(—)1s_L stored in the first and second memories 75 and 76. The failure determination section 77 determines a ratio between Vout_fsq_(—)1s_L and Vout_fsq_(—)1s_H. If the ratio of Vout_fsq_(—)1s_L/Vout_fsq_(—)1s_H is less than a predetermined value RVFLS_BR, it indicates that a difference between the sensor output in the state in which the element temperature is high and the sensor output in the state in which the element temperature is low is small. This means that the sensor output hardly increases when the element temperature decreases. Therefore, it is determined that the O2 sensor is faulty. On the other hand, if the ratio of Vout_fsq_(—)1s_L/Vout_fsq_(—)1s_H is equal to or greater than the predetermined value RVFLS_BR, the failure determination section 77 determines that the O2 sensor is normal.

[0090] If it is determined that the O2 sensor is normal, a flag F_O2BR is set to zero. If it is determined that the O2 sensor is faulty, the flag F_O2BR is set to one. When the value of the flag F_O2BR is one, an MIL (warning light) may be lit to inform a passenger that the O2 sensor is faulty.

[0091] Structure of Element Temperature Controller

[0092]FIG. 13 is a control block diagram of a controller for controlling the element temperature of the O2 sensor in accordance with one embodiment of the present invention. An object to be controlled or a plant of the element temperature control is the O2 sensor 17. Since it is difficult to directly measure the element temperature of the O2 sensor, the element temperature is estimated by an estimator 82. The estimator 82 calculates an estimated element temperature To2_hat based on the operating state of the internal combustion engine and an energization duty ratio DUTY that is determined in the previous cycle by a controller 81.

[0093] The estimated temperature To2_hat that is determined by the estimator 82 and a target element temperature To2_R are compared to determine an error Ec. The controller 81 determines the energization duty ratio DUTY for a heater based on the error Ec. The heater is provided in the O2 sensor 17. The heater is driven in accordance with the calculated energization duty ratio DUTY.

[0094] Thus, the controller 81 carries out feedback control for determining the duty ratio DUTY of energization of the heater so that the estimated temperature To2_hat converges to the target element temperature To2_R. In other words, feedback control for determining the duty ratio DUTY of energization of the heater is performed so that the error Ec between the estimated element temperature To2_hat and the target element temperature To2_R converges to zero.

[0095] The controller 81 carries out the feedback control using a response assignment control. By using the response assignment control, the accuracy and quick response of the control are maintained at high level. Especially, when the element temperature is reduced to a temperature lower than a normal temperature that is used for the normal operating state of the engine, the element temperature may overshoot toward a lower temperature and the O2 sensor may be inactivated. When the element temperature is increased to a temperature higher than the normal temperature, the heater may be damaged by overshoot of the heater temperature. According to the response assignment control, since the rate of convergence of the controlled variable to the target value can be designated, it is prevented that the O2 sensor is inactivated and that the heater is damaged.

[0096] The O2 sensor 17, which is an object to be controlled, can be modeled as shown in equation (7). The temperature To2 of the O2 sensor is defined as control output and the duty ratio DUTY of energization of the heater is defined as control input. The element of the O2 sensor is exposed to the exhaust gas, and is heated by the heater. Therefore, the element temperature To2 is determined based on the exhaust gas temperature Tex and the energization duty ratio that is calculated in the previous cycle.

[0097] The O2 sensor 17 is modeled as a discrete-time system model. Such modeling can make the algorithm of the element temperature control simple and suitable for computer processing.

To2(k+1)=Ao2{To2(k)−Tex(k)}+Bo2·DUTY(k)   (7)

[0098] Here, Ao2 and Bo2 are model parameters that are pre-identified with simulation or the like. Here, “k” is an identifier for identifying a control cycle. (k) indicates a current cycle and (k+1) indicates a next cycle.

[0099] Since it is difficult to directly measure the temperature To2 of the O2 sensor as described above, the estimated element temperature To2_hat calculated by the estimator 82 is used instead of the actual temperature To2. Since it is also difficult to directly measure the temperature Tex of the exhaust gas, an estimated exhaust gas temperature Tex_hat calculated by the estimator 82 is used instead of the actual exhaust gas temperature Tex.

[0100] An element temperature error Ec(k) is expressed as shown in the equation (8).

Ec(k)=To2_hat(k)−To2_R(k)   (8)

[0101] The controller 81 determines a switching function “σ” as shown in equation (9). The switching function specifies convergence behavior of the element temperature error Ec. Here, “pole” is a setting parameter of the switching function “σ”, and is set to satisfy “−1<pole<1”.

σ(k)=−pole·Ec(k−1)+Ec(k)   (9)

[0102] The equation in the case of σ(k)=0 is called an equivalent input system, which specifies convergence characteristics of the element temperature error Ec or controlled variable. Assuming σ(k)=0, the equation (9) is transformed to the equation (10). $\begin{matrix} {{{Ec}\left( {k - 1} \right)} = {\frac{1}{pole} \cdot {{Ec}(k)}}} & (10) \end{matrix}$

[0103] Now, characteristics of the switching function σ will be described. In FIG. 14, the equation (10) is shown as a line 85 on a phase space with Ec(k−1) on the horizontal axis and Ec(k) on the vertical axis. This line 85 is referred to as a switching line. It is assumed that an initial value of a state quantity (Ec(k), Ec(k−1)) that is a combination of Ec(k) and Ec(k−1) is shown by a point 86. The response assignment control operates to place the state quantity shown by the point 86 on the switching line 85 and then restrain it on the switching line 85.

[0104] According to the response assignment control, since the state quantity is held on the switching line 85, the state quantity can highly stably converge to the origin 0 of the phase space without being affected by disturbances or the like. In other words, by restraining the state quantity (Ec(k), Ec(k−1)) on such a stable system having no input as shown in the equation (10), the estimated element temperature To2_hat can converge to the target element temperature TO2_R robustly against disturbances and modeling errors.

[0105] In the embodiment, since the phase space in which the switching function σ is represented is two-dimensional, the switching line is a straight line 85. If the phase space is three-dimensional, the switching line is expressed by a plane. If the phase space is four-dimensional or n-dimensional where n is greater than four, the switching line is expressed by a hyperplane.

[0106] The setting parameter “pole” can be variably selected. Reduction (convergence) characteristics of the element temperature error Ec can be specified by the setting parameter “pole”.

[0107]FIG. 15 shows one example of response assignment characteristics of the response assignment control. A line 87 shows a case in which the value of the pole is “1”. A curve 88 shows a case in which the value of the pole is “0.8”. A curve 89 shows a case in which the value of the pole is “0.5”. As seen from the figure, the rate of convergence of the element temperature error Ec changes according to the value of the setting parameter “pole”. It is seen that the convergence rate becomes faster as the absolute value of “pole” becomes smaller.

[0108] In order to cause the estimated element temperature To2_hat to converge to the target element temperature To2_R, the controller 81 determines the control input DUTY (e.g., heater energization duty ratio) in accordance with equation (11). As described above, DUTY is input into the modeled object shown by the equation (7). Here, Krch, Kadp and Ko2 indicate feedback coefficients. The coefficients can be determined in accordance with the optimal control theory or the like. $\begin{matrix} {{{DUTY}(k)} = {{{Krch} \cdot {\sigma (k)}} - {{Kadp} \cdot {\sum\limits_{i = 0}^{k}\quad {\sigma (i)}}} - {{{Ko2} \cdot {To2\_ hat}}(k)}}} & (11) \end{matrix}$

[0109] A first term (proportional term of the switching function σ) in the equation (11) indicates a reaching law input for placing the state quantity on the switching line. A second term (integration term of the switching function σ) indicates an adaptive law input for placing the state quantity on the switching line while suppressing modeling errors and disturbances. A third term indicates an equivalent control input for restraining the state quantity on the switching line.

[0110] The estimator 82 calculates the estimated element temperature To2_hat in accordance with the following equation (12). The equation (12) is based on the model equation shown in equation (7). Here, Ao2 and Bo2 are the same as those shown in equation (7), and indicate estimated parameters that are predetermined based on simulation or the like.

To2_hat(k+1)=Ao2{To2_hat(k)−Tex_hat(k)}+Bo2·DUTY(k)   (12)

[0111] The estimated exhaust gas temperature Tex_hat(k) in the equation (12) is calculated in accordance with the following equation (13).

Tex_hat(k)=Kex·Tex_hat(k−1)+(1−Kex)·Tex_MAP[Ne(k), PB(k)]  (13)

[0112] Here, Tex_MAP

indicates a value extracted from a steady exhaust gas temperature map Tex_MAP based on the engine rotational speed Ne and the intake manifold pressure Pb. FIG. 16 shows one example of the steady exhaust gas temperature map Tex_MAP. The steady exhaust gas temperature map Tex_MAP stores estimated temperatures of the exhaust gas when the engine is in a steady operating state. Here, Kex indicates an estimated parameter that is predetermined with simulation or the like.

[0113] The estimated element temperature To2_hat(k+1) calculated in the current cycle by the estimator 82 is used by the controller 81 so as to determine the energization duty ratio DUTY in the next cycle

[0114] Operation Flow

[0115] For the sake of easier understanding of flowcharts shown in FIGS. 18 through 21, a flow of the failure detection procedure in accordance with one embodiment of the invention is schematically shown in FIG. 17. In a first period, the element temperature is controlled to be maintained at a predetermined high temperature (e.g., 800°), which is a temperature used for the normal operating state of the engine. The O2 sensor output Vout is subjected to the filtering process and the statistical process.

[0116] In a second period after the first period has elapsed, control for reducing the element temperature to a predetermined low temperature (650° for example) is performed so as to detect a failure of the O2 sensor. In a third period after the second period has elapsed, the element temperature is controlled to be maintained at 650°. During a third period, the O2 sensor output Vout is subjected to the filtering process and the statistical process.

[0117]FIG. 18 shows a main routine for detecting a failure of the O2 sensor in accordance with one embodiment of the present invention. In step S101, the value of a completion flag F_CHK is checked. The completion flag is a flag that is to be set to one when the failure determination process is completed. When the routine is carried out for the first time, the failure determination process has not yet been completed. Therefore, the answer of the determination step S101 is “No.”

[0118] In step S102, it is determined whether the value of a sensor activation flag is one. The sensor activation flag is a flag that is to be set to one when the O2 sensor is activated. If the value of the sensor activation flag is zero, a predetermined value TMFSTWT is set in a timer TMFLTST (S103). Time (e.g., 1.0 second) required to stabilize the output of the band-pass filter is set in the predetermined value TMFSTWT. In step S104, the completion flag F_CHK is set to zero.

[0119] In steps S105 through 107, predetermined initial values are respectively set in timers TMBRCHK1, TMBRCHK2 and TMBRCHK3. The three timers measure the first, second and third periods, respectively. In step S108, flags and variables used for controlling the element temperature are initialized. In step S109, the statistically processed sensor output Vout_fsq_(—)1s, which is to be calculated by the successive least squares method (FIG. 19), and a variable “P” are initialized.

[0120] If the value of the sensor activation flag is one in step S102 when the routine is re-entered, the O2 sensor output Vout is subjected to the filtering process in accordance with equation (1) to determine Vout_f(k) (S109). In step S110, in order to detect a state in which the vehicle is at cruise, a low pass filter is applied to vehicle speed Vp in accordance with the following equation (14) to determine a filtered vehicle speed Vflt. Here, afl, . . . , afn and bf0, . . . , bfm are low pass filter coefficients. A Butterworth filter or the like can be used as the low pass filter.

Vflt(k)=afl·Vflt(k−1)+, . . ., +afn·Vflt(k−n)+bf0·Vp(k)+, . . . +bfm·Vp(k−m)   (14)

[0121] In step S111, it is determined whether the timer TMFLTST activated in the step S103 indicates zero. If the timer does not indicate zero, the process proceeds to step S105, in which the first through third timers and the flags are initialized. If the timer indicates zero, it is determined whether O2 feedback control is being carried out (S112). If the O2 feedback control is being carried out, the process proceeds to step S113. Thus, when the output of the band-pass filter is stabilized and the air-fuel ratio is appropriately controlled by the O2 feedback control, the failure detection for the O2 sensor is carried out.

[0122] In step S113, the filtered vehicle speed Vflt(k) in the current cycle and the filtered vehicle speed Vflt(k−1) in the previous cycle are compared to determine whether a change in the vehicle speed is greater than a predetermined value X_DVLM. If the change in the vehicle speed is greater than the predetermined value X_DVLM, it indicates that the current operating state of the engine is not appropriate for carrying out the failure detection for the O2 sensor. Therefore, the process proceeds to step S105. In step S114, it is determined whether the engine rotational speed Ne is within a predetermined range (between a lower limit value X_NEL and an upper limit value X_NEH). If the engine rotational speed NE is not within the predetermined range, it indicates that the current operating state of the engine is not appropriate for carrying out the failure detection for the O2 sensor. Therefore, the process proceeds to step S105. In step S115, it is determined whether the intake manifold pressure PB is within a predetermined range (between a lower limit value X_PBL and an upper limit value X_PBH). If the intake manifold pressure PB is not within the predetermined range, it indicates that the current operating state of the engine is not appropriate for carrying out the failure detection for the O2 sensor. Therefore, the process proceeds to step S105.

[0123] If all of the answers of the determination steps S113 through S115 are “Yes,” the process proceeds to step S116, in which the successive least squares method is applied to the filtered sensor output Vout_f(k) (FIG. 19). The element temperature is then controlled in step S117 (FIG. 21).

[0124] If the completion flag F_CHK is one in step S101 when the routine is re-entered, the process proceeds to step S117 without making the failure determination. In step S117, the element temperature is controlled. Thus, the failure determination is carried out only once in a given driving cycle. The element temperature control is constantly carried out irrespective of the failure determination of the O2 sensor.

[0125]FIG. 19 shows a routine of the successive least squares process carried out in step S116. In step S121, the filtered sensor output Vout_f(k) is squared in accordance with equation (2) to determine Vout_fsq. In step S122, it is determined whether the timer TMBRCHK1 that measures the first period during which the element temperature is maintained at a high temperature indicates zero. If the timer does not indicate zero, a flag F_CHKH is set to one (S123). The flag F_CHKH has the value of one while the statistical process is carried out under the condition in which the element temperature is high.

[0126] In steps S124 through 127, the statistical process is carried out using the successive least squares method. In step S124, the error Eo2 is determined in accordance with equation (4). Vout_fsq_(—)1s shown in step S124 indicates a statistically processed sensor output determined in the previous cycle. In step S125, the gain coefficient KP is determined in accordance with equation (5). Here, “P” shown in step S125 has been calculated in the previous cycle in accordance with equation (6). In step S126, “P” that is to be used in the next cycle is calculated.

[0127] In step S127, the statistically processed sensor output Vout_fsq_(—)1s is calculated using the error Eo2 and the gain coefficient KP calculated in steps S124 and S125 in accordance with equation (3). When step S128 is carried out for the first time, the value of the flag F_CHKH is one. Therefore, the value of the calculated Vout_fsq_(—)1s is stored in a memory as Vout_fsq_(—)1s_H (S129).

[0128] If the first period has elapsed when the routine is re-entered, the answer of the determination step S122 is “Yes.” The process proceeds to step S130, in which it is determined whether the timer TMBRCHK2 that measures the second period during which the element temperature is changed from a high temperature to a low temperature indicates zero. If the timer does not indicate zero, the flag F_CHKH is set to zero to indicate that the first period has elapsed. A flag F_CHKW is set to one to indicate that the second period is in progress (S131). The statistical process should not be carried out while the element temperature is being changed. In step S139, the statistically processed sensor output Vot_fsq_(—)1s and the variable P are initialized. The process then exits the routine.

[0129] If the second period has elapsed when the routine is re-entered, the answer of the determination step S130 is “Yes.” The process proceeds to step S132, in which it is determined whether the timer TMBRCHK3 that measures the third period during which the element temperature is maintained at a low value indicates zero. If the timer does not indicate zero, the flag F_CHKW is set to zero to indicate that the second period has elapsed. A flag F_CHKL is set to one to indicate that the third period is in progress (S133).

[0130] In steps S124 through 127, as with the first period, the statistically processed sensor output Vout_fsq_(—)1s is calculated by the successive least squares method. In the third period, since the value of the flag F_CHKH is maintained at zero, the answer of the determination step S128 is “No.” The process proceeds to step S134, in which the value of Vout_fsq_(—)1s calculated in step S127 is stored in a memory as Vout_fsq_(—)1s_L.

[0131] If the third period has elapsed when the routine is re-entered, the answer of the determination step S132 is “Yes.” The process proceeds to step S135, in which the flag F_CHKL is set to zero to indicate that the third period has elapsed.

[0132] In both states in which the element temperature is high and low, the statistically processed sensor outputs Vout_fsq_(—)1s_L and Vout_fsq_(—)1s_H are determined. In step S136, a ratio of the two sensor outputs is calculated by the equation of RVFLS=Vout_fsq_(—)1s_L/Vout_fsq_(—)1s_H. In step S137, the failure determination is carried out based on the calculated ratio RVFLS (FIG. 20). When the failure determination is completed, the completion flag F_CHK is set to one (S138).

[0133]FIG. 20 shows a failure determination routine carried out in step S137 shown in FIG. 19. In step S141, if the calculated ratio RVFLS is less than a predetermined value RVFLS_BR, it is determined that the O2 sensor is faulty. The failure flag F_O2BR is set to one (S142). In step S141, if the calculated ratio RVFLS is equal to or greater than the predetermined value RVFLS_BR, it is determined that the O2 sensor is normal, exiting the routine.

[0134]FIG. 21 shows an element temperature control routine carried out in step S117 shown in FIG. 18. In step S151, it is determined whether the engine is in the starting mode. If the engine is in the starting mode, a delay timer TMO2H is set to a predetermined value TMO2DLY (e.g., 10 seconds) (S152). When the engine is in the starting mode, water included in exhaust gas may hit the element of the O2 sensor. If the element temperature is abruptly increased when the element temperature is cooled by water, the O2 sensor may be damaged. Therefore, the element temperature is maintained at a predetermined value To2R_AEST (e.g., 600°) until the predetermined time TMO2DLY elapses (S153).

[0135] If the engine is not in the starting mode in step S151 and the period TMO2DLY set in the delay timer TMO2H has elapsed in step S154, the process proceeds to step S155. In step S155, if either the flag F_CHKL or the flag F_CHKW is zero, it indicates that the first period is in progress. In the first period, the element temperature is maintained at a high value as described above. In step S156, the target element temperature To2_R is set to a predetermined high temperature TO2R_HI (e.g., 800°).

[0136] In step S155, if both the flags F_CHKL and F_CHKW are one, it indicates that the third period is in progress. In step S162, the target element temperature To2_R is set to a predetermined low temperature TO2R_LO (e.g., 650°).

[0137] In step S157, the element temperature error Ec is determined in accordance with equation (8). The estimated element temperature To2_hat shown in step S157 indicates an estimated element temperature To2_hat(k) calculated in the previous cycle. In step S158, the value of the switching function σ is determined in accordance with equation (9). In step S159, the energization duty ratio DUTY is calculated in accordance with equation (11). The estimated element temperature shown in step S159 also indicates the estimated element temperature To2_hat(k) calculated in the previous cycle.

[0138] In step S160, the estimated exhaust gas temperature Tex_hat(k) is calculated based on the estimated exhaust gas temperature Tex_hat(k−1) calculated in the previous cycle and the operating state of the engine (which is typically represented by intake manifold pressure Pb and engine rotational speed Ne) in the current cycle in accordance with equation (13). In step S161, the estimated element temperature To2_hat(k+1) is calculated based on the estimated element temperature To2_hat(k) calculated in the previous cycle, the estimated exhaust gas temperature Tex_hat(k) calculated in step S160, and the energization duty ratio DUTY(k) calculated in step S159 in accordance with equation (12). The calculated estimated element temperature To2_hat(k+1) is used for determining the energization duty ratio in the next cycle.

[0139] In the embodiment described above, the element temperature of the exhaust gas sensor is controlled from a high temperature to a low temperature. However, the present invention is not limited to the embodiment. The present invention can also be applied to the control for increasing the element temperature from a low temperature to a high temperature.

[0140] The element temperature and the exhaust gas temperature are determined by the estimator in the above embodiment. Alternatively, a temperature sensor may be disposed on an appropriate location. The element temperature and the exhaust gas temperature may be determined based on the temperature detected by the sensor.

[0141] The element temperature may be controlled using another appropriate control so as to detect a failure of the exhaust gas sensor.

[0142] The invention may be applied to an engine to be used in a vessel-propelling machine such as an outboard motor in which a crankshaft is disposed in the perpendicular direction. 

What is claimed is:
 1. An apparatus for detecting a failure of an exhaust gas sensor disposed in an exhaust manifold of an engine, the apparatus comprising a control unit configured to: compare detection values of the exhaust gas sensor, the detection values obtained under different temperatures of an element provided in the exhaust gas sensor; and detect the failure of the exhaust gas sensor based on the comparison result.
 2. The apparatus of claim 1, wherein the control unit is further configured to control an element temperature of the exhaust gas sensor, wherein the states of the different element temperatures are generated by the control of the element temperature.
 3. The apparatus of claim 1, further comprising a filter for filtering the detection values of the exhaust gas sensor, wherein the comparison is performed based on the filtered detection values.
 4. The apparatus of claim 3, wherein the filter includes a band-pass filter.
 5. The apparatus of claim 1, wherein the states of the different element temperatures at least include a state in which the element temperature is controlled to a first temperature for a normal operating state of the engine, and a state in which the element temperature is controlled to a second temperature lower than the first temperature.
 6. The apparatus of claim 1, wherein the control unit is further configured to apply a statistical process to the detection values of the exhaust gas sensor using a successive least squares method, wherein the comparison is performed based on the statistically processed detection values.
 7. The apparatus of claim 1, further comprising a filter for filtering the detection values of the exhaust gas sensor, wherein the control unit is further configured to apply a statistical process to the filtered detection values using a successive least squares method, wherein the comparison is performed based on the statistically processed detection values.
 8. The apparatus of claim 1, wherein the detection values of the exhaust gas sensor are obtained when a vehicle on which the engine is mounted is at cruise.
 9. The apparatus of claim 1, wherein the detection values of the exhaust gas sensor are obtained when the engine is in a predetermined operating state.
 10. The apparatus of claim 2, wherein the exhaust gas sensor further comprises a heater for heating the element, wherein the control unit is further configured to estimate the element temperature of the exhaust gas sensor, and to determine a duty ratio of energization of the heater based on the estimated element temperature.
 11. The apparatus of claim 2, wherein the exhaust gas sensor further comprises a heater for heating the element, wherein the control unit is further configured to determine a duty ratio of energization of the heater using response assignment control.
 12. A method for detecting a failure of an exhaust gas sensor disposed in an exhaust manifold of an engine, the method comprising the steps of: comparing detection values of the exhaust gas sensor, the detection values obtained under different temperatures of an element provided in the exhaust gas sensor; and detecting the failure of the exhaust gas sensor based on the comparison result.
 13. The method of claim 12, further comprising the step of controlling an element temperature of the exhaust gas sensor, wherein the states of the different element temperatures are generated by the control of the element temperature.
 14. The method of claim 12, further comprising the step of filtering the detection values of the exhaust gas sensor, wherein the comparison is performed based on the filtered detection values.
 15. The method of claim 14, wherein the filter includes a band-pass filter.
 16. The method of claim 12, wherein the states of the different element temperatures at least include a state in which the element temperature is controlled to a first temperature for a normal operating state of the engine, and a state in which the element temperature is controlled to a second temperature lower than the first temperature.
 17. The method of claim 12, further comprising the step of applying a statistical process to the detection values of the exhaust gas sensor using a successive least squares method, wherein the comparison is performed based on the statistically processed detection values.
 18. The method of claim 12, further comprising the steps of: filtering the detection values of the exhaust gas sensor; and applying a statistical process to the filtered detection values using a successive least squares method, wherein the comparison is performed based on the statistically processed detection values.
 19. The method of claim 12, wherein the detection values of the exhaust gas sensor are obtained when a vehicle on which the engine is mounted is at cruise.
 20. The method of claim 12, wherein the detection values of the exhaust gas sensor are obtained when the engine is in a predetermined operating state.
 21. The method of claim 13, wherein the exhaust gas sensor further comprises a heater for heating the element, wherein the step of controlling the element temperature further comprises the steps of: estimating the element temperature of the exhaust gas sensor; and determining a duty ratio of energization of the heater based on the estimated element temperature.
 22. The method of claim 13, wherein the exhaust gas sensor further comprises a heater for heating the element, wherein the step of controlling the element temperature further comprises the step of determining a duty ratio of energization of the heater using response assignment control.
 23. A computer program stored on a computer readable medium for use in detecting a failure of an exhaust gas sensor disposed in an exhaust manifold of an engine, the computer program comprising: program code for comparing detection values of the exhaust gas sensor, the detection values obtained under different temperatures of an element provided in the exhaust gas sensor; and program code for detecting the failure of the exhaust gas sensor based on the comparison result.
 24. The computer program of claim 23, further comprising program code for controlling an element temperature of the exhaust gas sensor, wherein the states of the different element temperatures are generated by the control of the element temperature.
 25. The computer program of claim 23, further comprising program code for filtering the detection values of the exhaust gas sensor, wherein the comparison is performed based on the filtered detection values.
 26. The computer program of claim 25, wherein the filter includes a band-pass filter.
 27. The computer program of claim 23, wherein the states of the different element temperatures at least include a state in which the element temperature is controlled to a first temperature for a normal operating state of the engine, and a state in which the element temperature is controlled to a second temperature lower than the first temperature.
 28. The computer program of claim 23, further comprising program code for applying a statistical process to the detection values of the exhaust gas sensor using a successive least squares method, wherein the comparison is performed based on the statistically processed detection values.
 29. The computer program of claim 23, further comprising: program code for filtering the detection values of the exhaust gas sensor; and program code for applying a statistical process to the filtered detection values using a successive least squares method, wherein the comparison is performed based on the statistically processed detection values.
 30. The computer program of claim 23, wherein the detection values of the exhaust gas sensor are obtained when a vehicle on which the engine is mounted is at cruise.
 31. The computer program of claim 23, wherein the detection values of the exhaust gas sensor are obtained when the engine is in a predetermined operating state.
 32. The computer program of claim 24, wherein the exhaust gas sensor further comprises a heater for heating the element, wherein the program code for controlling the element temperature further comprises: program code for estimating the element temperature of the exhaust gas sensor; and program code for determining a duty ratio of energization of the heater based on the estimated element temperature.
 33. The computer program of claim 24, wherein the exhaust gas sensor further comprises a heater for heating the element, wherein the program code for controlling the element temperature further comprises program code for determining a duty ratio of energization of the heater using response assignment control. 